X-ray emission of Mkn 421 and jet microphysics

Mkn 421 (z = 0.031) is the brightest blazar at X-ray and UV wavelengths and the brightest and most highly variable extragalactic TeV source. In the last few years it has been target of several BeppoSAX long lasting campaigns. The unprecedented quality of these recent observations allows to study in great detail the variability of the extreme tail of the synchrotron component, emitted by the highest energy electrons. This provides us with an important means to put some precise constraints on the energies of the relativistic electrons and on the physical parameters of the plasma within the jet, and for the first time meaningfully constrain (though only qualitatively) the time dependent particle injection/acceleration process. We summarize the main findings of the 1998 campaign, and briefly present the 1999 and 2000 campaigns, that with their continuous coverage will enable us to study the variability in even greater detail.